LAS VEGAS — A last-minute federal court battle over caucus rules demonstrates just how important a tight three-way Democratic presidential contest in Nevada has become in the battle for momentum headed into Super Tuesday’s votes. Hillary Rodham Clinton, Barack Obama and John Edwards are in a statistical dead heat in polling here before Saturday’s caucuses. And Nevada’s sizable blocs of Hispanic, union and urban voters could provide an indicator of where the race is headed on Feb. 5, when hundreds of delegates will be awarded in states with significant minority populations. By contrast, Republican candidates have stayed away from the diverse electorate and unfamiliar electoral landscape as Nevada voters weigh in earlier than ever before. No major GOP candidate has set foot in the state for two months, and some Republicans are bracing for a possible surprise first-place showing by long-shot Texas Rep. Ron Paul, the only Republican to broadcast TV ads in Nevada. At issue in a federal court hearing Thursday is whether Democratic caucuses will be held in nine casinos along the Las Vegas Strip. The special locations were designed to make it easier for housekeepers, waitresses and bellhops in the state’s biggest industry to caucus at midday near their jobs rather than returning home to neighborhood precincts. The rules were unanimously approved by the state Democratic party last March and ratified by the Democratic National Committee in August. But last Friday, six Democrats and a teachers union, which has ties to the Clinton campaign, sued to shut the sites on grounds they allocate too many delegates to one group. Of roughly 10,000 delegates to Nevada’s presidential nominating convention, more than 700 could be selected at casino caucuses, depending upon turnout, which could make them more valuable than some sparsely populated Nevada counties, the lawsuit said. Four plaintiffs are on the committee that approved the sites. The DNC petitioned to join the suit on behalf of the state party Tuesday. The Clinton campaign has denied any involvement in the lawsuit, but Obama noted it was filed two days after he was endorsed by the powerful Culinary Workers Union Local 226, which has organized many workers along the Strip. The union is the state’s largest with 60,000 members, more than 40 percent Hispanic. The Illinois senator drew cheers at a Culinary Union event Sunday when he said the rules were fine until the union decided, ‘‘I’m going to support the guy who’s standing with the working people instead of the big shots.’’ By Monday, Bill Clinton was defending the lawsuit. ‘‘I think the rules ought to be the same for everybody,’’ the former president told high school students near Las Vegas. The Culinary Union circulated a less subtle message on fliers to members: ‘‘Backers of Hillary Clinton are suing in court to take away our right to vote in the caucus.’’ It’s airing the same message in Spanish-langauge radio ads. The legal dustup is not the only sign that stakes have risen here as a new survey this week by the Reno Gazette-Journal showed the race is a toss-up among the three main rivals. Democratic campaign offices are packed with field workers from Iowa and New Hampshire. An Obama phone bank has been expanded into a parking lot trailer. New Clinton staffers are wearing name tags. The Edwards campaign tripled its staff. First to arrive after New Hampshire, Clinton went straight to a heavily Culinary Union neighborhood and found several members willing to break with the union to support her. The fight over labor has dominated the campaign partly because its proven organizing ability is one of the few tested elements in the contest. Party officials are hoping 40,000 people turn out, 10 percent of the state’s registered Democrats. Four years ago, a record 9,000 turned out. Clinton has the support of the Democratic establishment thanks to her state chairman, Clark County Commission Chairman Rory Reid, Sen. Harry Reid’s son. The New York senator lined up the boldface names in each demographic group, particularly among Hispanics, who are nearly 25 percent of the population. She went after regular party activists, women and hordes of retirees with time to work the phones. Edwards locked down some early union support, but the former North Carolina senator wrestled hard and lost when he needed it most. Along with the Culinary Union, the Nevada chapter of the Service Employees International Union aligned with Obama. The Edwards campaign has focused on a badly needed win in South Carolina and did not rush to match the stepped-up Obama and Clinton efforts. Before his labor endorsements, Obama’s campaign was fueled by new voters, blacks and scores of out-of-state canvassers from California and Arizona. His workers reached out to the massive work force on the Las Vegas Strip in casino employee breakrooms and cafeterias. Obama has tripled his television advertising and added a new commercial about his union endorsements. Clinton’s ads have highlighted her promise to close the proposed nuclear waste dump at Yucca Mountain, but all three candidates vied at a debate Tuesday to express the deepest opposition to the dump. Among Republicans, Paul had has TV and radio advertising almost all to himself. While he hasn’t placed higher than fourth in previous contests, his views are a natural fit among some in libertarian-leaning Nevada. Former Massachusetts Gov. Mitt Romney has made a play for support among fellow Mormons, a politically active community in Nevada. He has some radio ads, the only other Republican broadcasting ads here. A poll for the Gazette-Journal showed John McCain at 22 percent, Rudy Giuliani at 18 percent, Mike Huckabee with 16 percent and Romney at 15 percent. While Las Vegas and Reno receive the most attention, Obama and Clinton plan trips to Elko, a small ranching and mining town in northeast Nevada — part of their effort to scoop up voters left without a candidate when New Mexico Gov. Bill Richardson quit the race. Richardson’s departure also provided an opening among Hispanic voters in Las Vegas and fueled concentration on the Culinary Union. The heavily Hispanic union has been working members for two months, prompting signs this 24-hour town may tire of political attention. One graveyard shift worker last week posted this message to union canvassers outside a home: ‘‘Yes! We are caucusing with the Culinary ... Please do not knock (sleeping).’’

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